
theorem BPA:
  for a,b be positive Real, n be light positive Real holds
  a to_power n + b to_power n > (a + b) to_power n
  proof
    let a,b be positive Real, n be light positive Real;
    reconsider m = 1 - n as Real;
    a to_power (m+n) + b to_power (m+n) = (a + b) to_power (m+n);
    hence thesis by NEW;
  end;
